KC Border's notes on selected topics in mathematical economics
Colleagues and students:
In the previous millennium, I began to put my course
“handouts” on the web instead of handing them out. Here
is an index of many of them. I offer no warranty as to the
correctness of these notes, but I am not aware of any remaining errors.
However, many of them are incomplete. Feel free to use them in your
courses or studies, but do so at your own risk. Or as Ronald Reagan
was fond of saying, “Trust, but verify.”
I add to this list on occasion. The file sizes and dates
below reflect the latest uploads. The revision date in the handout
reflects only major revisions. If I find typos, reformat a few
equations, or simply play around with different fonts, I may upload
the new version without changing the revision date in the text. I am
now adding a time stamp to the handouts that indicates the last time
the file was converted to pdf from LaTeX. This is usually an
indication that something has changed, even if only the format. In
November of 2015, I began to update the first pages to reflect
the new Caltech Identity Project's recommendations on the use of the new
logo, so almost all file modification dates are 2015 or later, despite
the fact that some of these notes date back to the early 1980s and
were converted from
I'd appreciate it if you let me
know if you find any mistakes, or if you just find something too
obscure. Corrections are also greatly appreciated.
Rational choice and demand theory
Introductory notes on stochastic
and conditions that guarantee the equivalence of preference maximization
and expenditure minimization.
From the point of view of competitive demand theory,
local nonsatiation is
no more general than monotonicity. It took me thirty years
to notice this.
Neoclassical demand theory, as
you might find in Samuelson's Foundations, but with
slightly more modern notation.
Duality and demand theory.
The weak axiom of revealed
preference implies negative semidefiniteness of the Slutsky
Partial notes on Hurwicz and Uzawa's approach to the
Review of demand theory.
A crib sheet for qualifying exams.
of deriving demand functions, indirect utilities, and
expenditure functions from utility functions in the full
n-good case. Includes Cobb–Douglas (logarithmic and
exponential versions), linear, Leontief, quasi-linear
Cobb–Douglas; with accurate pictures of indifference
Cost and production
Introduction to the Arrow–Debreu–McKenzie–Nikaidô
Notes on boundedness of the set of
Statement and proof of the
First Welfare Theorem.
Statement and proof of the
Second Welfare Theorem.
Hurwicz's approach to the
Second Welfare Theorem via Saddlepoints.
Notes on the
core of an economy,
based on Debreu and Scarf and Richter.
(Non-)Existence of Walrasian Equilibrium.
Examples of what can go wrong when standard assumptions are
violated, plus a sketch of an existence proof based on the
excess demand approach.
Worked examples of computing Walrasian equilibria for
Robinson Crusoe economies.
Decision under uncertainty
Desultory notes on
including Dutch book arguments.
Notes on decision-making under uncertainty.
2016-12-07 [Similar to the Decision Theory note above; added by PJH from KCB's Ec121a course website]
Note on the de Finetti–Arrow–Pratt coefficient of
Growth & Economic Progress
[This section added by PJH from KCB's Ec140 course website]
The first-order linear differential equation
and its economic interpretation.
Maximization of a function of one variable.
of a function of several variables.
2018-10-03 Including the Lagrange
Implicit Function Theorem.
Increasing differences and comparative statics.
Euler's theorem on homogeneous functions.
Leibniz' rule for differentiating an integral.
Advanced integration by parts.
A bit sloppy in places.
Separating Hyperplane Theorems.
Supergradients and subgradients.
Theorem of the Alternative.
and constrained maximization.
Notes on the theory of
Linear Programming and saddlepoints.
Notes on the
and how to use it.
An example of a pointed, generating, finite cone in
R4 whose dual
cone has a different number of extreme rays, which I
prepared for Roko Aliprantis.
Metric spaces and topology
What you should remember about
2018-10-15 A list of terms
and results with almost no proofs.
Introduction to the basic concepts of point-set topology.
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